Matrix Games with Interval-Valued 2-Tuple Linguistic Information

In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is...

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Bibliographic Details
Published in:Games 2018-09, Vol.9 (3), p.62
Main Authors: Singh, Anjali, Gupta, Anjana
Format: Article
Language:English
Subjects:
2-tuple linguistic model
Computer & video games
Decision making
Fuzzy logic
Game theory
Games
interval-valued 2-tuple linguistic model
interval-valued linguistic matrix game
Linear programming
linguistic linear programming problem
Linguistics
Saddle points
Social networks
Variables
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Summary:In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.
ISSN:2073-4336
2073-4336
DOI:10.3390/g9030062